Tag Archives: K2

Shifting Eclipses – K2’s Second Multi-planet System

On March 20th this year, the moon will pass between Earth and the Sun sending a slither of Northern Europe into darkness. For those in the UK, this partial eclipse will be the most impressive eclipse until three minutes of totality at 4:56pm on September 23rd, 2090. Calculating something so far ahead seems like an impressive feat but in fact astronomers can precisely work out exactly when and where eclipses will occur for not just the next hundred, but the next million years. Such is the way for most transiting exoplanets too, the calculations for which could probably be valid in thousands of years.

477859main_KeplerSinglePanelStill[1]But a new planetary system, discovered by a team that includes Warwick astronomers (including me), doesn’t yet play by these rules. It consists of two planets orbiting their star, a late K star smaller than our sun, in periods of 7.9 and 11.9 days. The pair have radii 7- and 4-larger than Earth, putting them both between the sizes of Uranus and Saturn. They are the 4th and 5th planets to be confirmed in data from K2, the rejuvenated Kepler mission that monitors tens of thousands of stars looking for exoplanetary transits. (36 other planet candidates, including KIC201505350b & c, have been released previously).

But it is their orbits, rather than planetary characteristics, that have astronomers most excited. “The periods are almost exactly in a ratio of 1.5” explains Dave Armstrong, lead author of the study. This can be seen directly in how the star’s brightness changes over time. This lightcurve appears to have three dips of different depths, marked here by green, red and purple dips. ”Once every three orbits of the inner planet and two orbits of the outer planet, they transit at the same time”, causing the deep purple transits.

K2 Paper Lightcurve

But this doesn’t just make for an interesting lightcurve; the closeness of these periods to a 3/2 ratio also causes other weird effects. “The planets perturb each other and change their period every orbit, so they never quite transit when you expect”, explains Arms. These shifts are called Transit Timing Variations (or TTVs).

An Example of TTVs in a 2-planet system
TTVs in a 2-planet system (credit: Eric Ford)

The size of these TTVs is related to the mass of the planets, and some previous multi-planet systems have been weighed in this way. When the team went back to observe the larger planet less than 9 months later, they found that the transit time had shifted by more than an hour. And their period ratio of 1.5035 means the resulting TTVs are likely to continue increasing over a few years, potentially shifting the system more than a day from it’s current rhythm.

These TTVs also help prove that the planets are real. Their presence means that both objects are interacting with each other, so the planets must orbit the same star rather than being, say, two different background binaries. The team also used these shifts in transit time to constrain the planet masses, showing them to be less than 1.2 and 2.04 times that of Jupiter.

rvgif2[1]Not only is this one of the most interesting multi-planet systems yet discovered by Kepler, it is also one of the brightest (12th magnitude), making ground-based follow-up much easier than many Kepler systems. Most interestingly, precise spectrographs like HARPS and SOPHIE will be able to measure the tiny to-and-fro shift in the star’s velocity caused by the gravitation pull of planet on the star. This radial velocity would give a precise mass for the planets in the system and for the first time allow masses found by TTVs to be directly compared to those from RVs.

Fomalhaut_planet_341px[1]Examples of 3:2 resonance can be found everywhere in planetary science, including between Pluto & Neptune’s orbits, in the Kirkwood gap of the Asteroid Belt, and even between the planets around pulsar PSR1257+12. It is also thought that Jupiter and Saturn may have, at one point, become caught in a 3:2 resonance as they migrated inwards. This scenario, of planets caught in 3:2 resonance migrating inwards, could explain how these two sub-Jupiter sized planets came to be in such an unusual orbit.

These two planets could also help settle other dilemmas. “We’d like to answer questions like ‘Did they form there?’, ‘Did they migrate there and get stuck?’ and ‘will they eventually get ejected from the system, or crash into the star?’” suggests Armstrong. The best way to do this is simply by watching future transits and monitoring just how in-sync the planets really are. And maybe one day we could even begin to predict their eclipses as confidently as we can with those happening here on Earth.


The paper, submitted to A&A, can be found on ArXiV here. My work on the paper involved developing the tools to find the transiting planets in the K2 lightcurve.

Kepler’s Last Stand: Verification by Multiplicity

TNG_LaPalmaFor 3 months a year, the TNG telescope on the island of La Palma turns its high-precision spectrometer (HARPS-N) towards the constellations of Cygnus and Lyra. This is the field of view that NASA’s Kepler space telescope stared at for more than 3 years, detecting thousands of potential new exoplanets using the transit method. There the TNG scans hundreds of Kepler’s potentially planet-holding stars looking for tiny changes in their radial velocity. If detected, this signal will indicate the presence of a real planet, confirming once and for all what Kepler first hinted at many months before. This is the process that, up until now, has been used to definitively find the majority of Kepler’s 211 planets.

New ‘discoveries’ in context

That appeared to change in the blink of an eye this week with the confirmation of 715 new planets using a new catch-all statistical technique. But how did the Kepler team confirm all these new worlds, and can they really be considered real planets?

Without further observations with instruments such as HARPS, Kepler’s 3000 planetary candidates cannot usually be called definite planets. This is because a number of other signals could mimic the transit signal of a star, including tightly bound double-stars that graze one other as they orbit, or unseen dim stars that have binary companions. Alternatively the cameras themselves could be acting up, producing periodic, transit-like signals in the data. Last year a team used simulations of the Kepler data to estimate that around 10% of the candidates were likely to be such false positives.

Kepler Candidates by size

So how can more than 700 worlds be confirmed at once, without any manual work from telescopes on the ground? The answer is through performing statistics on Kepler’s planets. Of a zoo of 190,000 stars observed, Kepler discovered 3000 potential planets, of which 10% are likely to be spurious signals. As a rough estimate then (and the Kepler team go into much more effort than this), the random probability of finding a false positive is 300/190,000, or a rate of only 0.16%.

That number on its own cannot help confirm planets. The trick comes when thinking about Kepler’s hundreds of multiple planet systems. The likelihood of a single-planet system randomly having another false positive also in the data is extremely low. In fact, applying that rough number to the 1000 best single-planet candidates tells us only around 2 of those multiplanet systems should have a spurious planet. Similar calculations can be done for even rarer systems with two false positives, two planets and a false positive, etc.

Possible False Positve Signals

This rate can also be significantly improved by excluding any targets more likely to give these spurious signals. For example, the authors removed more than 350 potential planets from the initial sample for many reasons. Some had instrumental artefacts seen in other stars or had transits close to the limit of detection. Others with V-shaped transits were eliminated as these are more likely to be grazing binary stars. The team also studied the images Kepler took to check for possible transits on a secondary star, eliminating anything where the transit did not in the star’s central position.

Using these cuts, the study narrowed down the search to 851 planets around 340 stars. Applying statistics and using the estimate that 10% of currently detected planets might be false positives, the team found that 849 of the 851 planets were likely to be planets. This corresponds to a certainty of 99.8%,  just greater than 3σ, which in astronomy is usually enough to constitute a detection. This is how “verification by multiplicity” works.

Confirmed Kepler Planets by Size

Of these, 715 are previously un-confirmed worlds. Nearly all are relatively small planets, with radii going from the same as Earth up to that of Neptune. Four of these new planets may also reside in their star’s habitable zone, the region where liquid water could exist on the surface.

As amazing as it would be to nearly double the number of exoplanets overnight, some doubts remain about this method. By eliminating astronomical follow-ups, no extra information can be gleaned. For example, without performing radial velocity measurements, the mass of these planets will never be known. And without other accurate astronomical studies, we cannot accurately determine the nature of the star, and therefore the radius of the planet.

The main difference, though, comes from the impersonal nature of verification by multiplicity. Previous confirmation methods assessed the probability of each candidate being a planet individually. By performing the confirmation in bulk we will know, thanks to the statistics, that at least 2 planets are imposters*. But if exoplanet astronomers can learn to live with that doubt, such planets may well be accepted as confirmed worlds and this simple idea will see the single biggest influx of validated exoplanets in history.

* Here’s another way to compare those statements. Imagine you have two pills. One produces a 0.2% chance of death. The other causes the loss of two fingers (0.2% body mass). By adding these planets to the list of exoplanets, we may well gain a whole new body of worlds, but there will be painful amputations to come in the future.

The two papers, which will be released on March 10th in ApJ, can be found here (Lissauer, 2014) and here (Rowe, 2014).

UPDATE: The new planets are proving reasonably contentious. The exoplanet counter on NASA’s planetquest sits at 1690 , wheras the Paris-based exoplanet.eu remains on 1078. Time will tell whether astronomers accept these as true planets or simply string candidates.